---
title: "Reactive power injection and generation limits"
subject: "Power System Analysis II"
chapter: 1
key: "semester_5/power_system_analysis_ii:reactive-power-injection-limits"
source: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/reactive-power-injection-limits
site: BCT Engineering
---

# Reactive power injection and generation limits

Power System Analysis II · Chapter 1: Interconnected Power System

- Asked in: 2082 Baishakh, 3+5 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/reactive-power-injection-limits
- Whole chapter: https://www.bctengineer.com/md/semester_5/power_system_analysis_ii/chapter-1

## Question

What is the role of reactive power injection or consumption in a specified bus? For a synchronous generator connected to infinite bus discuss the concept of maximum and minimum reactive power generation limit.

## Short answer

Reactive power injection raises bus voltage; consumption lowers it. For a generator on an infinite bus, changing excitation varies Q at constant terminal voltage. Maximum Q is limited by field heating and armature current; minimum Q by steady-state stability (δ ≤ 90°) and end-region heating.

## Answer

#### Role of reactive power injection or consumption at a bus
Bus voltage depends mainly on the net reactive power at that bus, since $\Delta V \approx QX/V$ for a line with $X \gg R$.
- **Injecting Q** at a bus (generator over-excited, capacitor, condenser) reduces the reactive current drawn over the lines, so the **voltage rises**.
- **Consuming Q** at a bus (inductive load, reactor, under-excited generator) increases the drop across line reactance, so the **voltage falls**.

So Q injection/absorption is the main tool to hold the bus voltage at its specified value; this is why a PV bus has its Q left free (within limits) to keep $|V|$ fixed.

#### Generator on an infinite bus
For a cylindrical-rotor generator with internal emf $E_f$, terminal voltage $V$ (fixed by the infinite bus), synchronous reactance $X_s$ and load angle $\delta$:

$$
P = \frac{E_fV}{X_s}\sin\delta,\qquad
Q = \frac{E_fV\cos\delta - V^2}{X_s}
$$

With P fixed by the turbine, Q is set by the excitation $E_f$:
- $E_f\cos\delta > V$ (over-excited): Q > 0, generator **supplies** Q (lagging pf).
- $E_f\cos\delta < V$ (under-excited): Q < 0, generator **absorbs** Q (leading pf).

#### Maximum reactive power limit
The upper limit is set by **field (rotor) heating**. The maximum field current gives $E_{f,max}$, so

$$
Q_{max} = \frac{V}{X_s}\sqrt{E_{f,max}^2 - \left(\frac{PX_s}{V}\right)^2} - \frac{V^2}{X_s}
$$

On the P–Q capability chart this is a circle of radius $VE_{f,max}/X_s$ centred at $(0, -V^2/X_s)$. At high P, the **armature current limit** (circle of radius $VI_{a,max}$ about the origin) may set the bound instead.

#### Minimum reactive power limit
When the generator is under-excited:
1. **Steady-state stability limit:** as $E_f$ is reduced, $\delta$ increases for the same P; at $\delta = 90^\circ$ the machine loses synchronism. A practical margin (e.g. $\delta \le 70^\circ$) defines the limit.
2. **Stator end-region heating** in under-excited operation, which further restricts absorption.
3. A minimum excitation limit set by the exciter.

```text
        Q (supplied)
        ^    field-heating limit
        |  .---.
        | /     \  armature-current limit
  ------+--------+-----> P
        | \     /  stability / end-heating limit
        |  '---'
        v Q (absorbed)
```

So in load-flow studies a PV bus has $Q_{min} \le Q_G \le Q_{max}$; if a limit is hit, Q is fixed at that limit and the bus is treated as a PQ bus.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Injecting Q at a bus:
   A. lowers voltage
   B. raises its voltage
   C. changes frequency
   D. has no effect
   Answer: B. It reduces reactive current drawn over line reactance. (Key point: Injection effect)

2. With E_f cos(delta) > V, the generator:
   A. absorbs Q
   B. supplies zero Q
   C. supplies Q at lagging pf
   D. operates at leading pf
   Answer: C. Over-excited machines supply Q. (Key point: Over-excitation)

3. The maximum Q limit is set mainly by:
   A. steady-state stability
   B. stator end heating
   C. governor droop
   D. field heating (maximum Ef) or armature current
   Answer: D. These thermal limits bound Q supply. (Key point: Maximum Q limit)

4. If a PV bus hits its Q limit in load flow:
   A. Q is fixed at the limit and the bus is treated as PQ
   B. |V| is kept fixed
   C. P is fixed
   D. bus is removed
   Answer: A. Voltage can no longer be held. (Key point: PV bus limit)

## Related in Power System Analysis II

- [Generator reactive power at constant terminal voltage](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Agenerator-reactive-power-infinite-bus) — Power System Analysis II, chapter 1
- [Role of interconnection and reactive power control](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Ainterconnection-reactive-control) — Power System Analysis II, chapter 1
- [Rotor angle and swing equation, infinite bus](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Arotor-angle-swing-equation) — Power System Analysis II, chapter 6
- [Critical clearing angle/time, fault at infinite bus](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Acritical-clearing-infinite-bus-h5) — Power System Analysis II, chapter 6
- [Critical clearing, fault at infinite bus, H = 6](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Acritical-clearing-fault-infinite-bus-h6) — Power System Analysis II, chapter 6
- [3-bus load flow with Q limits (cut off)](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aload-flow-reference-load-generator-bus) — Power System Analysis II, chapter 2

## Related in other subjects

- [Generator on infinite bus with 15% excitation rise](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Agenerator-infinite-bus-excitation-15) — Electric Machines II, chapter 1
- [Power transfer and pf of motor on infinite bus](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Amotor-infinite-bus-power-transfer) — Electric Machines II, chapter 2
- [Nepal generation and consumption trends](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Anepal-generation-trend-5-years) — Power Plant Design, chapter 1
- [Infinite bus and HVDC vs HVAC comparison](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Ainfinite-bus-hvdc-vs-hvac) — Power System Analysis I, chapter 1